Question: Solve for $x$ : $6\sqrt{x} + 2 = 8\sqrt{x} + 7$
Subtract $6\sqrt{x}$ from both sides: $(6\sqrt{x} + 2) - 6\sqrt{x} = (8\sqrt{x} + 7) - 6\sqrt{x}$ $2 = 2\sqrt{x} + 7$ Subtract $7$ from both sides: $2 - 7 = (2\sqrt{x} + 7) - 7$ $-5 = 2\sqrt{x}$ Divide both sides by $2$ $\frac{-5}{2} = \frac{2\sqrt{x}}{2}$ Simplify. $-\dfrac{5}{2} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.